Question

Choose the graphic representation of the quadratic function f(x) = x2 – 8x + 24.

Answer 1

Refer the attached figure for the graphic representation of the given quadratic equation.

Step-by-step explanation:

Given expression:

    $f(x)=x^{2}-8 x+24$

To find:

  The graphic representation of the given quadratic function

For solution, plot the graph to the given quadratic equation.

The standard form of the equation is

  $y=a x^{2}+b x+c$

When comparing with given quadratic equation,

a = 1, b = - 8, c = 24

Axis of symmetry is $x=\frac{-b}{2 a}$

By applying the values, the axis of symmetry of given equation is

     $x=\frac{-(-8)}{2(1)}=4$

The vertex form of quadratic equation is $f(x)=a(x-h)^{2}+k$

Where, (h,k) are the vertex.

Convert the quadratic equation into vertex form.

By completing the square,

$f(x)=x^{2}-8 x+24$

$f(x)=\left(x^{2}-2(4) x+4^{2}\right)-4^{2}+24$

$f(x)=(x-4)^{2}+8$

On comparison,

(h , k) = (4 , 8)

Now, plot the equation with vertex (4,8) [refer attached figure].